The Ages of Six Members on a Board of Directors

The ages of six members on a board of directors of a nonprofit organization are shown
below. $\begin{array}{r|cccccc}\text { Member } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\\hline \text { Age } & 32 & 52 & 43 & 64 & 41 & 50\end{array}$
Consider these board members to be a population of interest. The table below shows all of the possible samples of size four. For each sample, the people in the sample, their ages, and the sample mean are listed. Use the table to find the mean of the variable $\bar { x }$ .
$\begin{array}{c|l|l}\text { Sample } & \text { Ages } & \bar{x} \\\hline \text { A, B, C, D } & 32,52,43,64 & 47.75 \\\text { A, B, C, E } & 32,52,43,41 & 42 \\\text { A, B, C, F } & 32,52,43,50 & 44.25 \\\text { A, B, D, E } & 32,52,64,41 & 47.25 \\\text { A, B, D, F } & 32,52,64,50 & 49.5 \\\text { A, B, E, F } & 32,52,41,50 & 43.75 \\\text { A, C, D, E } & 32,43,64,41 & 45 \\\text { A, C, D, F } & 32,43,64,50 & 47.25 \\\text { A, C, E, F } & 32,43,41,50 & 41.5 \\\text { A, D, E, F } & 32,64,41,50 & 46.75 \\\text { B, C, D, E } & 52,43,64,41 & 50 \\\text { B, C, D, F } & 52,43,64,50 & 52.25 \\\text { B, C, E, F } & 52,43,41,50 & 46.5 \\\text { B, D, E, F } & 52,64,41,50 & 51.75 \\\text { C, D, E, F } & 43,64,41,50 & 49.5\end{array}$